The asymptotic (non)equivalence of canonical and microcanonical ensembles, describing systems with soft and hard constraints respectively, is a central concept in statistical physics. Traditionally, ...the breakdown of ensemble equivalence (EE) has been associated with nonvanishing relative canonical fluctuations of the constraints in the thermodynamic limit. Recently, it has been reformulated in terms of a nonvanishing relative entropy density between microcanonical and canonical probabilities. The earliest observations of EE violation required phase transitions or long-range interactions. More recent research on binary networks found that an extensive number of local constraints can also break EE, even in absence of phase transitions. Here we study for the first time ensemble nonequivalence in weighted networks with local constraints. Unlike their binary counterparts, these networks can undergo a form of Bose–Einstein condensation (BEC) producing a core–periphery structure where a finite fraction of the link weights concentrates in the core. This phenomenon creates a unique setting where local constraints coexist with a phase transition. We find surviving relative fluctuations only in the condensed phase, as in more traditional BEC settings. However, we also find a non-vanishing relative entropy density for all temperatures, signalling a breakdown of EE due to the presence of an extensive number of constraints, irrespective of BEC. Therefore, in presence of extensively many local constraints, vanishing relative fluctuations no longer guarantee EE.
•Ensemble nonequivalence is found in weighted networks.•The presence of local constraints always leads the ensemble nonequivalence.•Bose-Einstein condensation can break the ensemble equivalence in weighted networks.
Abstract
The asymptotic equivalence of canonical and microcanonical ensembles is a central concept in statistical physics, with important consequences for both theoretical research and practical ...applications. However, this property breaks down under certain circumstances. The most studied violation of ensemble equivalence requires phase transitions, in which case it has a ‘restricted’ (i.e. confined to a certain region in parameter space) but ‘strong’ (i.e. characterized by a difference between the entropies of the two ensembles that is of the same order as the entropies themselves) form. However, recent research on networks has shown that the presence of an extensive number of local constraints can lead to ensemble nonequivalence (EN) even in the absence of phase transitions. This occurs in a ‘weak’ (i.e. leading to a subleading entropy difference) but remarkably ‘unrestricted’ (i.e. valid in the entire parameter space) form. Here we look for more general manifestations of EN in arbitrary ensembles of matrices with given margins. These models have widespread applications in the study of spatially heterogeneous and/or temporally nonstationary systems, with consequences for the analysis of multivariate financial and neural time-series, multi-platform social activity, gene expression profiles and other big data. We confirm that EN appears in ‘unrestricted’ form throughout the entire parameter space due to the extensivity of local constraints. Surprisingly, at the same time it can also exhibit the ‘strong’ form. This novel, simultaneously ‘strong and unrestricted’ form of nonequivalence is very robust and imposes a principled choice of the ensemble. We calculate the proper mathematical quantities to be used in real-world applications.
In the exploration of chiral solvating agents (CSAs) for nuclear magnetic resonance (NMR) spectroscopy designed for the chiral analysis of amino acid derivatives, notable advancements have been made ...with thiourea-CSAs.
, derived from 2-(1
)-1-aminoethylphenol and benzoyl isothiocyanate, is effective in the enantiodifferentiation of
-3,5-dinitrobenzoyl (
-DNB) amino acids. In order to broaden the application of
for configurational assignment, enantiomerically enriched
-DNB amino acids were analyzed via NMR. A robust correlation was established between the relative position of specific
H and
C NMR resonances of the enantiomers in the presence of
. 1,4-Diazabicyclo2.2.2octane (DABCO) was selected for the complete solubilization of amino acid substrates. Notably, the
and
protons of the
-DNB moiety displayed higher frequency shifts for the (
)-enantiomers as opposed to the (
)-enantiomers. This trend was consistently observed in the
C NMR spectra for quaternary carbons bonded to NO
groups. Conversely, an inverse correlation was noted for quaternary carbon resonances of the carboxyl moiety, amide carbonyl, and methine carbon at the chiral center. This observed trend aligns with the interaction mechanism previously reported for the same chiral auxiliary. The configurational correlation can be effectively exploited under conditions of high dilution or, significantly, under sub-stoichiometric conditions.
Nuclear magnetic resonance (NMR) spectroscopy is an analytical technique largely applied in the analysis of discrimination processes involving enantiomeric substrates and chiral agents, which can ...interact with the analyte either via covalent bonding or via formation of diastereomeric solvates. However, enantiodiscrimination has been observed, in some cases, even in the absence of any additional chiral selector. The reasons behind this phenomenon must be found in the capability of some chiral substrates to interact with themselves by forming diastereomeric solvates in solution that can generate nonequivalences in the NMR spectra of enantiomerically enriched mixtures. As a result, differentiation of enantiomers is observed, thus allowing the quantification of the enantiomeric composition of the mixture under investigation. The tendency of certain substrates to self-aggregate and to generate diastereomeric adducts in solution can be defined as Self-Induced Diastereomeric Anisochrony (SIDA), but other acronyms have been used to refer to this phenomenon. In the present work, an overview of SIDA processes investigated via NMR spectroscopy will be provided, with a particular emphasis on the nature of the substrates involved, on the interaction mechanisms at the basis of the phenomenon, and on theoretical treatments proposed in the literature to explain them.
Unbiased sampling of network ensembles Squartini, Tiziano; Mastrandrea, Rossana; Garlaschelli, Diego
New journal of physics,
02/2015, Letnik:
17, Številka:
2
Journal Article
Recenzirano
Odprti dostop
Sampling random graphs with given properties is a key step in the analysis of networks, as random ensembles represent basic null models required to identify patterns such as communities and motifs. ...An important requirement is that the sampling process is unbiased and efficient. The main approaches are microcanonical, i.e. they sample graphs that match the enforced constraints exactly. Unfortunately, when applied to strongly heterogeneous networks (like most real-world examples), the majority of these approaches become biased and/or time-consuming. Moreover, the algorithms defined in the simplest cases, such as binary graphs with given degrees, are not easily generalizable to more complicated ensembles. Here we propose a solution to the problem via the introduction of a 'Maximize and Sample' ('Max & Sam' for short) method to correctly sample ensembles of networks where the constraints are 'soft', i.e. realized as ensemble averages. Our method is based on exact maximum-entropy distributions and is therefore unbiased by construction, even for strongly heterogeneous networks. It is also more computationally efficient than most microcanonical alternatives. Finally, it works for both binary and weighted networks with a variety of constraints, including combined degree-strength sequences and full reciprocity structure, for which no alternative method exists. Our canonical approach can in principle be turned into an unbiased microcanonical one, via a restriction to the relevant subset. Importantly, the analysis of the fluctuations of the constraints suggests that the microcanonical and canonical versions of all the ensembles considered here are not equivalent. We show various real-world applications and provide a code implementing all our algorithms.
In this paper, we first derive a theoretical basis for spherical conformal parameterizations between a simply connected closed surface
S
and a unit sphere
S
2
by minimizing the Dirichlet energy on
C
...¯
with stereographic projection. The Dirichlet energy can be rewritten as the sum of the energies associated with the southern and northern hemispheres and can be decreased under an equivalence relation by alternatingly solving the corresponding Laplacian equations. Based on this theoretical foundation, we develop a modified Dirichlet energy minimization with nonequivalence deflation for the computation of the spherical conformal parameterization between
S
and
S
2
. In addition, under some mild conditions, we verify the asymptotically R-linear convergence of the proposed algorithm. Numerical experiments on various benchmarks confirm that the assumptions for convergence always hold and demonstrate the efficiency, reliability and robustness of the developed modified Dirichlet energy minimization.
Theories of tonal music take for granted that all keys of the same mode (i.e., all major and all minor keys) are employed by composers in essentially the same way; however, newer analytical and ...cognitive research challenges this view by pointing to aspects of transpositional nonequivalence among the keys. The present study offers possibly the first systematic, data-driven investigation of correlations between the choice of absolute key and structure across a composer's body of works. By performing an extensive corpus-based analysis of music by Wolfgang Amadé Mozart (1756–91), we derive 55 prototypes, subsuming phenomena from three independent domains: dynamic-rhetoric gestures that launch orchestral works, digressions to the parallel minor in sonata-allegro movements, and the occurrences of a particular six-note motive across Mozart's complete oeuvre. Ten prototypes display a significant association with a specific key after correction for multiple comparisons, amounting to a statistically significant total. Investigation of key-related musical structure offers fresh insight into Mozart's compositional decisions and the relation between schemata and their instantiations in his works, at the same time suggesting a revised perspective on traditional key characteristics. Mozart's perfect pitch offers one possible explanation for the role of key-related structure in his works; however, we also contemplate other possible explanations.
Studies of thiamine diphosphate-dependent enzymes appear to have commenced in 1937, with the isolation of the coenzyme of yeast pyruvate decarboxylase, which was demonstrated to be a diphosphoric ...ester of thiamine. For quite a long time, these studies were largely focused on enzymes decarboxylating α-keto acids, such as pyruvate decarboxylase and pyruvate dehydrogenase complexes. Transketolase, discovered independently by Racker and Horecker in 1953 (and named by Racker) 1, did not receive much attention until 1992, when crystal X-ray structure analysis of the enzyme from Saccharomyces cerevisiae was performed 2. These data, together with the results of site-directed mutagenesis, made it possible to understand in detail the mechanism of thiamine diphosphate-dependent catalysis. Some progress was also made in studies of the functional properties of transketolase. The last review on transketolase, which was fairly complete, appeared in 1998 3. Therefore, the publication of this paper should not seem premature.
•The general structure of transketolase is described.•The mechanism of action of transketolase is described.•Optical characteristics of transketolase are given.•Transketolase heterogeneity is being discussed.•Future prospects of the study of transketolase are considered.
This essay proposes that the thought of rhetoricity, as the fundamental affectability and responsivity supposed in every rhetorical exchange, could offer an orientation through which to affirm an ...existence-in-common worthy of the name democracy. This coexistence, this being-together that is the demos, exceeds any possible figuration as well as any historical determination. Synced to the rhythms of another temporality, its kairotic eruptions open onto an unpredictable and unprogrammable future. It is from the affirmation of this existence-in-common that a truly democratic politics might begin to be imaginable, a politics faithful to this demos, and so to its fundamental repudiation of equivalence, calculability, exchangeability.
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